Large inter-die and intra-die process variations result in significant uncertainty in delay of circuits. Large delay variations may lead to parametric/functional failures. In this paper we propose a novel leakage-variation-tolerant online current monitor, namely leakage canceling current sensor, to detect completion of operations in logic blocks. The current monitor is applied to self-timed logic to design process variation tolerant circuits. It is observed that, for self-timed circuits, the probability of functional failures can be reduced by 50% with no performance degradation and with same power consumption.